Question

What are the asymptote(s) and hole(s), if any, of `f(x) =(sinx)/(5x^2+2x+1)`?

Answer 1

Please see below.

Explanation:

There are no holes and no vertical asymptotes because the denominator is never `0` (for real `x`).

Using the squeeze theorem at infinity we can see that `lim_(xrarroo)f(x) = 0` and also `lim_(xrarr-oo)f(x) = 0`, so the `x`-axis is a horizontal asymptote.